HEAVY TRAFFIC APPROXIMATIONS FOR A SYSTEM OF INFINITE SERVERS WITH LOAD BALANCING

Philip J. Fleming · Burton Simon

19 citations0/0 files storedProbability in the Engineering and Informational Sciences

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Advanced Queuing Theory Analysis Stochastic processes and statistical mechanics Probability and Risk Models

Abstract

We consider an exponential queueing system with multiple stations, each of which has an infinite number of servers and a dedicated arrival stream of jobs. In addition, there is an arrival stream of jobs that choose a station based on the state of the system. In this paper we describe two heavy traffic approximations for the stationary joint probability mass function of the number of busy servers at each station. One of the approximations involves state-space collapse and is accurate for large traffic loads. The state-space in the second approximation does not collapse. It provides an accurate estimate of the stationary behavior of the system over a wide range of traffic loads.

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1965Limiting diffusion approximations for the many server queue and the repairman problem 2006Some diffusion approximations with state space collapse 1967On limit laws for service processes in multi-channel systems 1997A heavy-traffic analysis of a closed queueing system with a GI/∞ service center 1984Heavy-Traffic Approximations for Service Systems With Blocking

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